Predicting the fluid mechanical characteristics of a gas-solid two-phase flow is critical for the successful design and operation of coal gasification systems, coal fired turbines, rocket nozzles, and other energy conversion systems. This work presents a general grid-free numerical solution which extends a numerical solution of the Navier-Stokes equations developed by Chorin to a solution suitable for unsteady or steady dilute gas-solid particle flows. The method is applicable to open or closed domains of arbitrary geometry. The capability of the method is illustrated by analyzing the flow of gas and particles about a cylinder. Good agreement is found between the numerical method and experiment.